A convex lens made up of glass of refractive index `1.5` is dippedin turn (i) in a medium of refractive index `1.65` (ii) in a medium of refractive index `1.33` (a) Will it behave as converging or diverging lens in the two cases ? (b) How will its focal length changes in the two media ?

A convex lens made up of glass of refractive index `1.5` is dippedin t

1.	A convex lens made up of glass of refractive index `1.5` is dippedin turn (i) in a medium of refractive index `1.65` (ii) in a medium of refractive index `1.33` (a) Will it behave as converging or diverging lens in the two cases ? (b) How will its focal length changes in the two media ?
Answer» Here,`.^(a)mu_(g)=1.5` Let `f_(air)` be the focal length of the lens in air, Then, `(1)/(f_(air))(.^(a)mu_(g)-1)((1)/(R_(1))-(1)/(R_(2)))` or `((1)/(R_(1))-(1)/(R_(2)))=(1)/(f_(air)(.^(a)mu_(g)-1))` `=(1)/(f_(air)(1.5-1))` or `((1)/(R_(1))-(1)/(R_(2)))=(2)/(f_(air)) .....(i)` (i) When lens is dipped in medium `A` Here, `.^(a)mu_(A)=1.65` Let `f_(A)` be the focal length of the lens, when dipped in medium `A`. Then, `(1)/(f_(A))(.^(A)mu_(g)-1)((1)/(R_(1))-(1)/(R_(2)))=((.^(a)mu_(g))/(.^(a)mu_(A))-1)((1)/(R_(1))-(1)/(R_(2)))` Using the equation `(i)`, we have `(1)/(f_(A))((1.5)/(1.65)-1)xx(1)/(f_(air))=-(1)/(5.5f_(air))` or `f_(A)=-5.5f_(air)` As the sign of `f_(A)` is opposite to that of `f_(air)` the lens will behave as a diverging lens. (ii) When lens is dipped in medium `B` : Here, `.^(a)mu_(B)=1.33` Let `f_(B)` be the focal length of the lens, when dipped in medium `B`. Then, `(1)/(f_(B))(.^(B)mu_(g)-1)((1)/(R_(1))-(1)/(R_(2)))=((.^(a)mu_(g))/(.^(a)mu_(B))-1)((1)/(R_(1))-(1)/(R_(2)))` Using the equation `(i)`, we have `(1)/(f_(B))((1.5)/(1.33)-1)xx(2)/(f_(air))=(0.34)/(1.33f_(air))` As the sign of `f_(B)` is same as that of `f_(air)` the lens will behave as a converging lens.

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A convex lens made up of glass of refractive index `1.5` is dippedin turn (i) in a medium of refractive index `1.65` (ii) in a medium of refractive index `1.33` (a) Will it behave as converging or diverging lens in the two cases ? (b) How will its focal length changes in the two media ?

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